Coherent-scattering two-dimensional cooling in levitated cavity optomechanics

The strong light-matter optomechanical coupling offered by coherent scattering set-ups have allowed the experimental realization of quantum ground-state cavity cooling of the axial motion of a levitated nanoparticle [U. Delić et al., Science 367, 892 (2020)]. An appealing milestone is now quantum two-dimensional (2D) cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarization, one obtains two nearly equivalent modes, with similar frequencies ω x ∼ ω y and optomechanical couplings g x ≃ g y —in this experimental configuration we identify an optimal trap ellipticity, nanosphere size, and cavity linewidth which allows for efficient 2D cooling. Moreover, we find that 2D cooling to occupancies n x + n y ≲ 1 at moderate vacuum ( 10 − 6 mbar) is possible in a “Goldilocks” zone bounded by √ κ Γ / 4 ≲ g x , g y ≲ ∣ ∣ ω x − ω y ∣ ∣ ≲ κ , where one balances the need to suppress dark modes while avoiding far-detuning of either mode or low cooperativities, and κ ( Γ ) is the cavity decay rate (motional heating rate). With strong-coupling regimes g x , g y ≳ κ in view one must consider the genuine three-way hybridization between x , y and the cavity light mode resulting in hybridized bright/dark modes. Finally, we show that bright/dark modes in the levitated set-up have a simple geometrical interpretation, related by rotations in the transverse plane, with implications for directional sensing

Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

Logics of knowledge and action: critical analysis and challenges

International audienceWe overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges